The passive vibration control of mechanical systems under unwanted vibrations can be accomplished in a very effective way by using devices incorporating viscoelastic materials. The design of such devices requires a broad knowledge of the dynamic properties of the employed viscoelastic material, usually supplied by adequate mathematical models. Among the available mathematical models, the fractional derivative (FD) model and the Golla-Hughes-McTavish (GHM) model, along with either the Williams-Landel-Ferry (WLF) equation or the Arrhenius equation, are now very prominent. The current work investigates the use of these models in a wide and integrated dynamic characterization of a typical and thermorheologically simple viscoelastic material. It focuses on experimental data collected from 0.1 to 100 Hz and-40 °C to 50 °C, which are simultaneously manipulated to raise both the frequency and the temperature dependencies of the material. In fitting the models, a hybrid approach-combining techniques of genetic algorithms and nonlinear optimization-is adopted. The ensuing results are evaluated by means of objective function values, comparative experimental-predicted data plots, and the Akaike's Information Criterion (AIC). It is shown that the four-parameter fractional derivative model presents excellent curve fitting results. As for the GHM model, its modified version is the most adequate, although a higher number of terms is required for a satisfactory goodness-of-fit. None the less the fractional derivative model stands out.
Viscoelastic materials are used to reduce vibrations in mechanical systems due to their control efficacy. Considering that the dynamic behavior of those materials may be described by means of complex moduli, and experimental data may present ucertainties, an alternative is to use probabilistic methods, especially the Bayesian inference approach. By that approach, probability distribution functions are obtained for parameters of a model which describes the behavior of a given material. The present work employs a viscoelastic material modeled by the Bayesian approach in two vibration control actions, namely: a) use of vibration isolators; b) use of dynamic neutralizers. Transmissibility and receptance curves are displayed as well as dimensions of the control devices. Performance predictions are carried out in both cases. It is shown that the Bayesian approach can favourably reflect the presence of the uncertainties and advance their effects. Thus, more information can be provided for the designer of viscoelastic vibration control devices to anticipate eventual corrective measures.
The dynamic behavior of a typical viscoelastic material in wide ranges of frequency and temperature is characterized. A four-parameter fractional derivative model was considered in the frequency domain along with the Arrhenius and WLF models, also for including temperature as a source of variation. A Bayesian framework is adopted and inferences on parameters governing the model quantities of interest are based on samples from posterior distributions obtained by Monte Carlo Markov Chain (MCMC) methods. Posterior predictive checks were conducted to ensure the goodness-of-fit of the model. Based on the results we argue that the Bayesian framework allows more complete and suitable inference about dynamic properties of typical viscoelastic materials, as required for broad and sound vibration control actions.
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